Definable Singularity
Copyright policy )Definable Singularity
The main result of this paper is a characterization of singular cardinals in terms of the core model, assuming that there is no model of ∃ κ o ( κ ) = κ + + \exists \kappa \,o(\kappa )= {\kappa ^{ + + }} . This characterization is used to prove a result in infinitary Ramsey theory. In the course of the proof we develop a simplified statement of the covering lemma for sequences of measures which avoids the use of mice. We believe that this development will be capable of isolating almost all applications of the covering lemma from the detailed structure of the core model.
Large cardinals, Inner models, including constructibility, ordinal definability, and core models, Other notions of set-theoretic definability, covering lemma for sequences of measures, infinitary Ramsey theory, core model, Consistency and independence results, singular cardinals
Large cardinals, Inner models, including constructibility, ordinal definability, and core models, Other notions of set-theoretic definability, covering lemma for sequences of measures, infinitary Ramsey theory, core model, Consistency and independence results, singular cardinals
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